Optimum solutions for a system of differential equations via measure of noncompactness |
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| Authors: | M Gabeleh J Markin |
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| Institution: | 1. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran;2. 528 Rover Blvd., Los Alamos, NM 87544, USA |
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| Abstract: | New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’s fixed point theorems. In the last section, we apply such results to study the existence of optimum solutions to a system of differential equations. |
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| Keywords: | Best proximity point (pair) Cyclic (noncyclic) condensing operator Optimum solution System of differential equations |
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